Unavoidable sample size issues beset psychological research that involves scarce populations or costly laboratory procedures. When incorporating longitudinal designs these samples are further reduced by traditional modeling techniques, which perform listwise deletion for any instance of missing data. Moreover, these techniques are limited in their…

Recently, studies have adopted fixed effects modeling to identify the returns to college. This method has the advantage over ordinary least squares estimates in that unobservable, individual-level characteristics that may bias the estimated returns are differenced out. But the method requires extensive longitudinal data and involves complex…

Children's understanding of numbers is often assessed using a number-line task, where the child is shown a line labeled with 0 at one end and a higher number (e.g., 100) at the other end. The child is then asked where on the line some intermediate number (e.g., 70) should go. Performance on this task changes predictably during childhood, and this…

How can children's natural perceptuo-motor skills be harnessed for teaching and learning mathematical structure? We address this question in the case of the integers. Existing research suggests that adult mental representations of integers recruit perceptuo-motor functionalities involving symmetry. Building on these findings, we designed a…

In this study, a cost function is used to estimate the costs for California districts to meet the achievement goals set out for them by the state. I calculate estimates of base costs (i.e., per pupil costs in a district with relatively low levels of student need) and marginal costs (i.e., the additional costs associated with specific student…